Derivation of the Maxwell-Schrödinger and Vlasov-Maxwell Equations from Non-Relativistic QED
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910694110134272 |
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| author | Leopold, Nikolai |
| author_facet | Leopold, Nikolai |
| contents | We study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of reduced density matrices, that the many-body quantum state converges to a tensor product of a semiclassically structured Slater determinant and a coherent photon state. These evolve according to a fermionic variant of the Maxwell-Schrödinger equations. By combining this result with [arXiv:2308.16074] through a suitable regularization of the initial data, we further show that, in the limit of large particle number, the dynamics of the Pauli-Fierz Hamiltonian can be approximately described by the non-relativistic Vlasov--Maxwell system for extended charges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivation of the Maxwell-Schrödinger and Vlasov-Maxwell Equations from Non-Relativistic QED Leopold, Nikolai Mathematical Physics Analysis of PDEs 35Q40, 35Q83, 81V10, 82C10 We study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of reduced density matrices, that the many-body quantum state converges to a tensor product of a semiclassically structured Slater determinant and a coherent photon state. These evolve according to a fermionic variant of the Maxwell-Schrödinger equations. By combining this result with [arXiv:2308.16074] through a suitable regularization of the initial data, we further show that, in the limit of large particle number, the dynamics of the Pauli-Fierz Hamiltonian can be approximately described by the non-relativistic Vlasov--Maxwell system for extended charges. |
| title | Derivation of the Maxwell-Schrödinger and Vlasov-Maxwell Equations from Non-Relativistic QED |
| topic | Mathematical Physics Analysis of PDEs 35Q40, 35Q83, 81V10, 82C10 |
| url | https://arxiv.org/abs/2411.07085 |